A very simple question I can't find in the scattered tetration literature.
If \( 1 < \alpha < e^{1/e} \) is \( ^z\alpha \) analytic in \( \alpha \)? I.e: is it expandable into a Taylor series in \( \alpha \) depending on \( z \) about each \( \alpha_0 \in (1,\eta) \)?
If \( 1 < \alpha < e^{1/e} \) is \( ^z\alpha \) analytic in \( \alpha \)? I.e: is it expandable into a Taylor series in \( \alpha \) depending on \( z \) about each \( \alpha_0 \in (1,\eta) \)?